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In the given figure, if AB || CD || EF, then the measure of ∠CEF is
- a)210°
- b)140°
- c)70°
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In the given figure, if AB || CD || EF, then the measure of∠CEF is...
Given
AB || CD || EF
∠ B = 70° and ∠ BCE = 30°
Calculation
AB || CD and BC is a transversal,
⇒ ∠ B = ∠ BCD [Alternate interior angles]
⇒ 70° = ∠ BCE + ∠ ECD
⇒ 70° = 30° + ∠ ECD
⇒ ∠ ECD = 70° - 30° = 40°
EF || CD and EC is a transversal
⇒ ∠ CEF + ∠ ECD = 180° [Sum of angles on same side of transversal is 180°]
⇒ ∠ CEF + 40° = 180°
⇒ ∠ CEF = 180° - 40° = 140°
∴ ∠ CEF = 140°
AB || CD || EF
∠ B = 70° and ∠ BCE = 30°
Calculation
AB || CD and BC is a transversal,
⇒ ∠ B = ∠ BCD [Alternate interior angles]
⇒ 70° = ∠ BCE + ∠ ECD
⇒ 70° = 30° + ∠ ECD
⇒ ∠ ECD = 70° - 30° = 40°
EF || CD and EC is a transversal
⇒ ∠ CEF + ∠ ECD = 180° [Sum of angles on same side of transversal is 180°]
⇒ ∠ CEF + 40° = 180°
⇒ ∠ CEF = 180° - 40° = 140°
∴ ∠ CEF = 140°
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In the given figure, if AB || CD || EF, then the measure of∠CEF isa)210°b)140°c)70°d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
Question Description
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